JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.

A triggering mechanism responsible for the explosive onset of edge localised modes (ELMs) in fusion plasmas is identified by performing, for the first time, non-linear magnetohydrodynamic simulations of repetitive type-I ELMs. Briefly prior to the ELM crash, destabilising and stabilising terms are affected at different timescales by an increasingly ergodic magnetic field caused by non-linear interactions between the axisymmetric background plasma and growing non-axisymmetric perturbations. The separation of timescales prompts the explosive, i.e. faster than exponential, growth of an ELM crash which lasts ∼ 500   μ s . The duration and size of the simulated ELM crashes compare qualitatively well with type-I ELMs in ASDEX Upgrade. As expected for type-I ELMs, a direct proportionality between the heating power in the simulations and the ELM repetition frequency is obtained. The simulations presented here are a major step forward towards predictive modelling of ELMs and of the assessment of mitigation techniques in ITER and other future tokamaks.

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